degree:8
 order:40
[ 8, 3, 12, 16 ][ 8, 0, 2, 0, 0, 6 ]

minimal polynomial:[ x-8, x, x+8, x^2-24 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-2*x-3
x^5-168*x^3+3456*x
x^3-12*x^2-64*x

 SITA:
[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 8, 0, 0, 0 ], [ 1, 0, 3, 0, 4 ], [ 0, 8, 0, 0, 0 ], [ 0, 0, 0, 0, 8 ], [ 0, 2, 0, 6, 0 ] ], 
  [ [ 0, 0, 3, 0, 0 ], [ 0, 3, 0, 0, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 3 ] ], 
  [ [ 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 12 ], [ 0, 0, 0, 12, 0 ], [ 1, 0, 3, 0, 8 ], [ 0, 6, 0, 6, 0 ] ], 
  [ [ 0, 0, 0, 0, 16 ], [ 0, 4, 0, 12, 0 ], [ 0, 0, 0, 0, 16 ], [ 0, 8, 0, 8, 0 ], [ 1, 0, 3, 0, 12 ] ] ]